An efficient unsupervised method for obtaining polygonal approximations of closed digital planar curves

• Approximations with the best balance between fidelity and efficiency are automatically obtained.
• The method has no parameter to be set.
• The method has an moderate algorithmic complexity (among O(NlogN) and O(N2)).

The contour of a shape is a powerful feature that enables its description and subsequent recognition. However, the direct use of a contour introduces redundancy. Many algorithms have been proposed for simplification of a contour while its most outstanding features are maintained. However, several inconveniences can be found in these methods, mainly the need for user interaction to set proper values for the parameters and, in some cases, for each specific contour. The proposed algorithm obtains polygonal approximations of contours and does not have parameters that must be adjusted, which provides the best balance between fidelity and efficiency, and has a modest algorithmic complexity. The method is based on an analysis of the convexity/concavity tree of the contour, and an efficient split/merge strategy is used. The experiments conducted show that the proposed method overcomes the state-of-the-art, using both synthetic data and a broad dataset of real contours.